The goal would be that neither the verification service nor the service you are verifying with can link the connection: the verification service can't tell which service you are connecting to, and the service you are verifying your age to can't determine your ID. The first two issues you mention don't necessarily seem to kill that (though I agree they are both suboptimal: once you are verified you should be able to generate your own verification keys without connecting to the verification service, and any requirement for attestation is just an unncessary restriction), though the revocation check does seem like it might be a problem.

The issue is that a lot of these services wave around a lot of words that _might_ mean that they are reasonably private, but it's damn hard to actually detemine if it is actually working like that in practice (the eIDAS standard seems to suggest the ZKP stuff is entirely optional, for example).